In the LP model the predicted mass of \(\chi _{c0}(4P)\) , \(M\simeq 4544\)  MeV,
is close to the mass of \(X(4500)\) , \(4506\pm 11^{+12}_{-15}\)  MeV.
Considering the \(X(4500)\)  as the \(\chi _{c0}(4P)\)  state, we study its strong decay
properties and the results are listed in Table REF .
It is shows that the calculated total
width, \(\Gamma \sim 50\)  MeV, is compatible with the measured value
of \(X(4500)\)  within its uncertainties. In Ref. [1]}, the \(X(4500)\)  was also
considered as the conventional \(\chi _{c0}(4P)\)  state in the coupled-channel approach.
If \(X(4500)\)  is the \(\chi _{c0}(4P)\)  state indeed,
it may dominantly decay into the \(DD_1\) , \(DD_1^{\prime }\) , \(D^*D_0\)  and \(D^*D_2\)  channels, and
the branching fractions are about \(\mathcal {O}(10\%)\) . In contrast, the decay rate into \(DD\)  channel is relatively small, which is
is predicted to be \(Br[X(4500)\rightarrow DD]\sim 10^{-3}\) . Such a small branching ratio may be difficult to observe
in experiment.
